制定刀架的加工工藝設(shè)計(jì)鉆M8底孔的鉆床夾具設(shè)計(jì)【軸承座】

制定刀架的加工工藝設(shè)計(jì)鉆M8底孔的鉆床夾具設(shè)計(jì)【軸承座】,軸承座,制定刀架的加工工藝,設(shè)計(jì)鉆M8底孔的鉆床夾具設(shè)計(jì)【軸承座】,制定,制訂,刀架,加工,工藝,設(shè)計(jì),m8,底孔,鉆床,夾具,軸承 機(jī) 械 加 工 工 藝 過 程 卡 片產(chǎn)品型號(hào)零（部）件圖號(hào)5-20第 頁產(chǎn)品名稱刀架零（部）件名稱共 頁材料牌號(hào)HT200毛坯種類普通灰口鑄鐵毛坯外形尺寸每毛坯件數(shù)1每臺(tái)件數(shù)備注工序號(hào)工序名稱工 序 內(nèi) 容車間工段設(shè)備工藝裝備工時(shí)準(zhǔn)終單件1鑄造 砂型鑄造,時(shí)效處理外協(xié)2清砂除去澆冒口、鋒邊及型砂外協(xié)3銑夾緊刀架孔兩側(cè)毛坯，銑刀架底面，照顧尺寸55mm和表面粗糙度，采用X51立式銑床加專用夾具。車間立式銑床銑夾具，量具，銑刀4銑以上下底面為基準(zhǔn)，并夾緊，銑后端面，采用X51銑床加專用夾具。車間立式銑床銑夾具，量具，銑刀5鉆以底面為基準(zhǔn)，夾緊前后端面，鉆11孔和16孔，保證16孔深為10mm，采用Z525鉆床加專用夾具。車間鉆床鉆夾具6鉆以底面為基準(zhǔn)，夾緊前后端面，鉆，鉸8孔，采用Z525鉆床加專用夾具。車間鉆床鉆夾具7鉆以底面為基準(zhǔn)，夾緊前后端面，鉆，鏜32孔，并保證孔中心到底面的距離為55mm和對(duì)孔的平行度，采用Z525鉆床和T616鏜床加專用夾具。車間鉆床鉆夾具8鉆以底面和后端面為基準(zhǔn)，夾緊兩側(cè)面，鉆M8螺紋底孔，攻M8螺紋，采用Z525鉆床加專用夾具。車間鉆床專用夾具9車車圓角R2和倒角1*45，采用CA6140車床和專用夾具。車間車床車床夾具，車刀10去毛刺質(zhì)管科11入庫檢驗(yàn)質(zhì)管科編制 （日期）審核 （日期）會(huì)簽 （日期）、處 數(shù)更改文件號(hào)簽字日期標(biāo)記處數(shù)更改文件號(hào)簽字日期 機(jī)械制造技術(shù)課程設(shè)計(jì)說明書設(shè)計(jì)題目：制定圖5-20所示刀架的加工工藝，設(shè)計(jì)鉆M8底孔的鉆床夾具 專 業(yè)： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 班 級(jí)： 學(xué) 號(hào)： 姓 名： 指導(dǎo)教師： 機(jī)械工程系2012年 12 月 14 日摘要 本次設(shè)計(jì)是刀架件的加工工藝規(guī)程及一些工序的專用夾具設(shè)計(jì)。刀架的主要加工表面是平面及孔。由加工工藝原則可知，保證平面的加工精度要比保證孔的加工精度容易。所以本設(shè)計(jì)遵循先面后孔的原則。并將孔與平面的加工明確劃分成粗加工和精加工階段以保證加工精度?；鶞?zhǔn)選擇以32孔作為粗基準(zhǔn)，以為刀架底面作為精基準(zhǔn)。主要加工工序安排是先以30孔為基準(zhǔn)加工出底面，再以底面定位加工出工藝孔。在后續(xù)工序中除個(gè)別工序外均用底面和工藝孔定位加工其他孔與平面。關(guān)鍵詞：刀架；加工工藝；專用夾具 目錄1零件的分析.4 1.1零件的作用4 1.2零件的工藝分析4 1.2.1零件圖.4 1.2.2 加工表面及孔52 確定零件的生產(chǎn)類型5 2.1 零件的生產(chǎn)類型5 2.2 毛坯的確定6 2.2.1 毛坯的種類及制造方法.6 2.2.2 確定鑄件加工余量.6 2.2.3 繪制毛坯圖.73 定位基準(zhǔn)的選擇.73.1 選擇粗基準(zhǔn).83.2 選擇精基準(zhǔn).84 制定機(jī)械加工工藝路線.84.1 確定各加工表面的加工方法.94.2 擬定加工工藝路線.95 機(jī)械加工余量，工序尺寸及公差的確定105.1 加工余量和工序尺寸的確定105.2 確定切削用量及時(shí)間定額116 夾具設(shè)計(jì) .297 參考文獻(xiàn) .31 1 零件的分析 1.1 零件的作用刀架是用于安裝車刀的零件，鏜孔的目的是為了和刀具相配合，臺(tái)階孔是用于固定刀架的，32孔是用來與刀具相連，支撐并固定刀具. 1.2 零件的工藝分析1.2.1零件圖：零件的三維圖，如下圖所示1.2.2加工表面及孔（1）32及8兩孔都具有較高的精度要求，表面粗糙度Ra的值是1.6um，是加工的關(guān)鍵表面。（2）刀架的下表面的表面粗糙度Ra為1.6um，16孔的下表面及內(nèi)孔的表面粗糙度Ra分別為3.2um和6.3um，以及刀架的后端面的表面粗糙度Ra為6.3um，是加工的重要表面，刀架的下表面與軸承孔中心線有平行度要求，0.01um，也是粗糙度的加工表面。（3）M8螺紋加工主要保證其定位尺寸的要求。（4）其余表面要求不高。2 確定零件的生產(chǎn)類型 2.1 零件的生產(chǎn)類型 零件的生產(chǎn)類型是指企業(yè)（或車間，工段，班組，工作地等）生產(chǎn)專業(yè)化程度的分類，它對(duì)工藝規(guī)程的制訂具有決定性的影響。生產(chǎn)類型一般可分為大量生產(chǎn)，成批生產(chǎn)和單件生產(chǎn)三種類型，不同的生產(chǎn)類型有著完全不同的工藝特性。零件的生產(chǎn)類型是按零件的年生產(chǎn)綱領(lǐng)和產(chǎn)品特征來確定的。生產(chǎn)綱領(lǐng)是指企業(yè)在計(jì)劃期內(nèi)應(yīng)當(dāng)生產(chǎn)的產(chǎn)品產(chǎn)量和進(jìn)度計(jì)劃。年生產(chǎn)綱領(lǐng)是包括備品和廢品在內(nèi)的年產(chǎn)量。零件的年生產(chǎn)綱領(lǐng)N可按下式計(jì)算：式中：N零件的生產(chǎn)類型（件/年）； Q產(chǎn)品的年產(chǎn)量（臺(tái)、輛）； m每臺(tái)（輛）產(chǎn)品中該零件的數(shù)量（件/臺(tái)、輛）； a備品率，一般取24； b廢品率，一般取0.30.7根據(jù)上式計(jì)算求得零件的生產(chǎn)綱領(lǐng)，通過查表可得刀架的生產(chǎn)類型為中批生產(chǎn)。2.2 毛坯的確定 2.2.1 確定毛坯的種類及其制造方法 零件的材料為HT150，考慮零件在機(jī)床運(yùn)行過程中所承受的沖擊不大，零件結(jié)構(gòu)又比較簡(jiǎn)單，生產(chǎn)類型為中批生產(chǎn)，毛坯可選用鑄造成型零件形狀不復(fù)雜，因此毛坯形狀可以與零件形狀盡量接近。2.2 2確定注件加工余量查機(jī)械制造工藝設(shè)計(jì)簡(jiǎn)明手冊(cè)，選用鑄件尺寸公差等級(jí)CT-12,選用加工余量為MA-H級(jí)，并根據(jù)毛坯的基本尺寸可知：刀架底面的機(jī)械加工余量為6.5mm，后端面的機(jī)械加工余量為6.5mm。 2.2.3 繪制鑄件毛坯圖3 定位基準(zhǔn)的選擇 正確地選擇定位基準(zhǔn)是設(shè)計(jì)工藝過程的一項(xiàng)重要內(nèi)容。也是保證零件加工精度的關(guān)鍵。定位基準(zhǔn)分為粗基準(zhǔn)、精基準(zhǔn)及輔助基準(zhǔn)。選擇定位基準(zhǔn)時(shí)，既要考慮零件的整個(gè)加工工藝過程，又要考慮零件的特征、設(shè)計(jì)基準(zhǔn)和加工方法，根據(jù)粗、精基準(zhǔn)的選擇原則，合理選定零件加工過程中的定位基準(zhǔn)。通常在制定工藝規(guī)程時(shí)，總是先考慮選擇怎樣的精基準(zhǔn)以保證達(dá)到精度要求并把各個(gè)表面加工出來，即先選擇零件表面最終加工所用精基準(zhǔn)和中間工序所用的精基準(zhǔn)，然后在考慮選擇合適的最初工序的粗基準(zhǔn)把精基準(zhǔn)面加工出來。3.1 選擇粗基準(zhǔn) 按照有關(guān)粗基準(zhǔn)的選擇原則，按照粗基準(zhǔn)的選擇原則：選擇要求加工余量小而均勻的重要表面的粗基準(zhǔn)，以保證該表面有足夠而均勻的加工余量。故選擇32外輪廓面為基準(zhǔn)，能方便的加工出32孔，保證孔中心與刀架下端面的平行度，32孔外輪廓面的面積較大，無澆口，冒口，飛邊等缺陷，符合粗基準(zhǔn)的要求。3.2 選擇精基準(zhǔn)經(jīng)分析零件圖可知，刀架底面為高度方向基準(zhǔn)，刀架前端面為寬度方向基準(zhǔn)，根據(jù)統(tǒng)一原則，考慮選擇以加工的刀架底面為精基準(zhǔn)，保證底面與孔32孔中心線的距離為55.，該基準(zhǔn)面積較大，工件的裝夾穩(wěn)定可靠，容易操作，夾具結(jié)構(gòu)也比較簡(jiǎn)單。4 制定機(jī)械加工工藝路線4.1 確定各加工表面的加工方法 該刀架的加工表面為：刀架的底面，后端面，32內(nèi)孔，11，16臺(tái)階孔，8通孔，M8螺紋。根據(jù)各加工表面尺寸精度及表面粗糙度要求，底面的加工路線為：粗銑-半精銑-精銑，后端面的加工路線為：粗銑-半精銑，32內(nèi)孔的加工路線為：粗鏜-精鏜，11孔的加工路線為：由于該表面的粗糙度要求比較低，直接采取鉆就可以了，16孔的加工路線為：鉆-粗鉸，8的加工路線為：鉆-粗鉸-精鉸，M8螺紋的加工路線為：鉆-攻螺絲。4.2 擬定加工工藝路線 根據(jù)零件的加工的幾何形狀，尺寸精度及位置精度，以及加工方法所能達(dá)到的經(jīng)濟(jì)精度，在生產(chǎn)綱領(lǐng)已確定的情況下，可以考慮采用萬能機(jī)床配以專用工具，并盡量使工序集中來提高生產(chǎn)率。查機(jī)械制造工藝設(shè)計(jì)簡(jiǎn)明手冊(cè)第20頁表1.4-7,1.4-8，1.4-11，選擇零件的加工工藝路線如下：工序 1：時(shí)效處理工序 2：除去澆冒口、鋒邊及型砂工序 3：夾緊刀架孔兩側(cè)毛坯，銑刀架底面，照顧尺寸55mm和表面粗糙度，采用X51立式銑床加專用夾具。工序 4：以上下底面為基準(zhǔn)，并夾緊，銑后端面，采用X51銑床加專用夾具。工序 5：以底面為基準(zhǔn)，夾緊前后端面，鉆11孔和16孔，保證16孔深為10mm，采用Z525鉆床加專用夾具。工序 6：以底面為基準(zhǔn)，夾緊前后端面，鉆，鉸8孔，采用Z525鉆床加專用夾具。工序 7：以底面為基準(zhǔn)，夾緊前后端面，鉆，鏜32孔，并保證孔中心到底面的距離為55mm和對(duì)孔的平行度，采用Z525鉆床和T616鏜床加專用夾具。工序 8：以底面和后端面為基準(zhǔn)，夾緊兩側(cè)面，鉆M8螺紋底孔，攻M8螺紋，采用Z525鉆床加專用夾具。工序 9：車圓角R2和倒角1*45，采用CA6140車床和專用夾具。工序 10：去毛刺工序 11：終檢，入庫。5 機(jī)械加工余量，工序尺寸及公差的確定5.1加工余量和工序尺寸的確定 前面根據(jù)資料已初步確定工件各表面的總加工余量，現(xiàn)在確定各表面的各個(gè)加工工序的加工余量的如下：加工表面加工內(nèi)容加工余量精度等級(jí)尺寸偏差表面粗糙度底面鑄件6.5CT123.5粗銑4IT1222.5-0.35012.5半精銑1.5IT11210-0.226.3精銑1IT7200-0.0351.6后端面鑄件6.5CT123.5粗銑5.5IT1266.50-0.3512.5半精銑1IT8610-0.0546.311鉆11IT12110+0.1812.516鉆15IT12160+0.1812.5精鉸1IT10150+0.073.28鉆7.8IT127.80+0.1512.5粗鉸0.16IT107.960+0.0583.2精鉸0.04IT880+0.0221.632粗鏜1.7IT1131.70+0.166.3精鏜0.3IT1732-0.03501.6M8鉆6.8IT1280+0.1512.5攻螺紋1.212.55.2確定切削用量及時(shí)間按定額工序2銑刀架底面1. 粗銑刀架底面 1.1加工條件 工件材料：45 b =160180MPa 鑄造 ；工件尺寸：aemax=60mm，l=104mm; 加工要求：粗銑刀架底面，加工余量為4mm， 機(jī)床：X51立式銑床 刀具：根據(jù)切削用量簡(jiǎn)明手冊(cè)（后稱切削手冊(cè)）表1.2，選擇YG硬質(zhì)合金端銑刀，根據(jù)表.3.1 ，銑削寬度為60mm，故根據(jù)銑削寬度ae60,深度ap6,齒數(shù)z=10,故根據(jù)機(jī)械制造工藝設(shè)計(jì)簡(jiǎn)明手冊(cè)（后簡(jiǎn)稱簡(jiǎn)明手冊(cè)）表3.1，取刀具直徑d0=80mm。根據(jù)切削用量手冊(cè)（后簡(jiǎn)稱切削手冊(cè)）表3.16，選擇刀具前角05后角08，副后角0=10，刃傾角：s=10,主偏角Kr=60,過渡刃Kr=30,副偏角Kr=5。1.2 切削用量1.2.1 確定切削深度 因?yàn)橛嗔枯^小，故選擇ap=4mm，一次走刀即可完成 1.2.2 確定每齒進(jìn)給量fz 由于本工序?yàn)榇旨庸ぃ叽缇群捅砻尜|(zhì)量可不考慮，從而可采用不對(duì)稱端銑，以提高進(jìn)給量提高加工效率。根據(jù)切削手冊(cè)表3.5，使用YG6硬質(zhì)合金端銑刀加工，機(jī)床功率為4.5kw（據(jù)簡(jiǎn)明手冊(cè)表4.2-35，X51立式銑床）時(shí)： fz=0.090.18mm/z故選擇：fz=0.18mm/z。1.2.3 確定刀具壽命及磨鈍標(biāo)準(zhǔn) 根據(jù)切削手冊(cè)表3.7，銑刀刀齒后刀面最大磨損量為1.5mm；由于銑刀直徑d0=80mm，故刀具使用壽命T=180min（據(jù)簡(jiǎn)明手冊(cè)表3.8） 1.2.4 計(jì)算切削速度vc和每分鐘進(jìn)給量vf 根據(jù)切削手冊(cè)表3.16，當(dāng)d0=100mm，Z=10，ap7.5，fz0.18mm/z時(shí)，vt=98m/min,nt=322r/min,vft=490mm/min。各修正系數(shù)為：kMV= 1.12，kSV= 0.8。切削速度計(jì)算公式為：其中 ，將以上數(shù)據(jù)代入公式：確定機(jī)床主軸轉(zhuǎn)速： 。根據(jù)簡(jiǎn)明手冊(cè)表4.2-36，選擇nc=380r/min,vfc=510mm/min,因此，實(shí)際進(jìn)給量和每分鐘進(jìn)給量為：vc=m/min=119m/minf zc=v fc/ncz=510/38010 mm/z=0.13mm/z1.2.5 校驗(yàn)機(jī)床功率 根據(jù)切削手冊(cè)表3.24，近似為Pcc=3.3kw,根據(jù)機(jī)床使用說明書，主軸允許功率Pcm=4.50.75kw=3.375kwPcc。故校驗(yàn)合格。最終確定:ap=4.0mm，nc=380r/min，vf=510mm/s，vc=119m/min，fz=0.13mm/z。1.2.6 計(jì)算基本工時(shí) tmL/ vf，L=l+ y+，l=104mm.查切削手冊(cè)表3. 26，入切量及超切量為：y+=12mm，則：tmL/ Vf=(104+12)/510=0.28min。2. 半精銑刀架底面 刀具：YG6硬質(zhì)合金端銑刀；機(jī)床：X51立式銑床；切削深度ap： 1.5mm ；查切削手冊(cè)表3.5，進(jìn)給量為：，取為0.5mm/r參考有關(guān)手冊(cè)，確定，采用YG6硬質(zhì)合金端銑刀，則：現(xiàn)采用X51立式銑床，根據(jù)簡(jiǎn)明手冊(cè)表4.2-36，取，故實(shí)際切削速度： 當(dāng)時(shí)，工作臺(tái)每分鐘進(jìn)給量：，取為980mm/min本工序切削時(shí)間為： 3. 精銑刀架底面 刀具：YG6硬質(zhì)合金端銑刀；機(jī)床：X51立式銑床；切削深度ap： 1.0mm ；查切削手冊(cè)表3.5，進(jìn)給量為：，取為0.4mm/r參考有關(guān)手冊(cè)，確定，采用YG6硬質(zhì)合金端銑刀，則：現(xiàn)采用X51立式銑床，根據(jù)簡(jiǎn)明手冊(cè)表4.2-36，取，故實(shí)際切削速度： 當(dāng)時(shí)，工作臺(tái)每分鐘進(jìn)給量：，取為980mm/min本工序切削時(shí)間為： 工序3 銑刀架后端面 1.粗銑刀架后端面 1.1加工條件 工件材料：HT150 b =160180MPa 鑄造 ；工件尺寸：aemax=80mm，l=104mm; 加工要求：粗銑刀架底面，加工余量為5.5mm， 機(jī)床：X51立式銑床 刀具：根據(jù)切削用量簡(jiǎn)明手冊(cè)（后稱切削手冊(cè)）表1.2，選擇YG硬質(zhì)合金端銑刀，根據(jù)表.3.1 ，銑削寬度為80mm，故根據(jù)銑削寬度ae90,深度ap6,齒數(shù)z=12,故根據(jù)機(jī)械制造工藝設(shè)計(jì)簡(jiǎn)明手冊(cè)（后簡(jiǎn)稱簡(jiǎn)明手冊(cè)）表3.1，取刀具直徑d0=125mm。根據(jù)切削用量手冊(cè)（后簡(jiǎn)稱切削手冊(cè)）表3.16，選擇刀具前角05后角08，副后角0=10，刃傾角：s=10,主偏角Kr=60,過渡刃Kr=30,副偏角Kr=5。1.2 切削用量1.2.1確定切削深度 因?yàn)橛嗔枯^小，故選擇ap=5.5mm，一次走刀即可完成 1.2.2 確定每齒進(jìn)給量fz 由于本工序?yàn)榇旨庸?，尺寸精度和表面質(zhì)量可不考慮，從而可采用不對(duì)稱端銑，以提高進(jìn)給量提高加工效率。根據(jù)切削手冊(cè)表3.5，使用YG6硬質(zhì)合金端銑刀加工，機(jī)床功率為4.5kw（據(jù)簡(jiǎn)明手冊(cè)表4.2-35，X51立式銑床）時(shí)： fz=0.090.18mm/z故選擇：fz=0.18mm/z。1.2.3 確定刀具壽命及磨鈍標(biāo)準(zhǔn) 根據(jù)切削手冊(cè)表3.7，銑刀刀齒后刀面最大磨損量為1.5mm；由于銑刀直徑d0=125mm，故刀具使用壽命T=180min（據(jù)簡(jiǎn)明手冊(cè)表3.8） 1.2.4 計(jì)算切削速度vc和每分鐘進(jìn)給量vf 根據(jù)切削手冊(cè)表3.16，當(dāng)d0=125mm，Z=12，ap7.5，fz0.18mm/z時(shí)，vt=98m/min,nt=322r/min,vft=490mm/min。各修正系數(shù)為：kMV= 1.12，kSV= 0.8。切削速度計(jì)算公式為：其中 ，將以上數(shù)據(jù)代入公式：確定機(jī)床主軸轉(zhuǎn)速： 。根據(jù)簡(jiǎn)明手冊(cè)表4.2-36，選擇nc=255r/min,vfc=300mm/min,因此，實(shí)際進(jìn)給量和每分鐘進(jìn)給量為：vc=m/min=100m/minf zc=v fc/ncz=300/（25510） mm/z=0.12mm/z1.2.5 校驗(yàn)機(jī)床功率 根據(jù)切削手冊(cè)表3.24，近似為Pcc=3.3kw,根據(jù)機(jī)床使用說明書，主軸允許功率Pcm=4.50.75kw=3.375kwPcc。故校驗(yàn)合格。最終確定:ap=5.5mm，nc=255r/min，vf=300mm/s，vc=100m/min，fz=0.12mm/z。1.2.6 計(jì)算基本工時(shí) tmL/ vf，L=l+ y+，l=104mm.查切削手冊(cè)表3. 26，入切量及超切量為：y+=17mm，則：tmL/ Vf=(104+17)/300=0.40min。2 半精銑刀架后端面 刀具：YG6硬質(zhì)合金端銑刀；機(jī)床：X51立式銑床；切削深度ap： 1mm ；查切削手冊(cè)表3.5，進(jìn)給量為：，取為0.5mm/r參考有關(guān)手冊(cè)，確定，采用YG6硬質(zhì)合金端銑刀，則：現(xiàn)采用X51立式銑床，根據(jù)簡(jiǎn)明手冊(cè)表4.2-36，取，故實(shí)際切削速度： 當(dāng)時(shí)，工作臺(tái)每分鐘進(jìn)給量：，取為980mm/min本工序切削時(shí)間為： 工序4 鉆，鉸11，16孔，保證孔的精度鉆1 鉆11孔通孔 1.1 鉆選擇鉆頭 根據(jù)切削手冊(cè)表2.1，2.2，選擇高速鋼麻花鉆頭，由于11孔的粗糙度要求較低，故以此粗鉆do=11mm，鉆頭采用雙錐后磨橫刀，后角o12， 2.選擇切削用量 2.1 確定進(jìn)給量按加工要求確定進(jìn)給量：查切削手冊(cè)，f=0.520.64 ，由切削手冊(cè)表2.7,系數(shù)為0.5,則： 按鉆頭強(qiáng)度選擇:查切削手冊(cè)表2.8,鉆頭允許進(jìn)給量為：；按機(jī)床進(jìn)給機(jī)構(gòu)強(qiáng)度選擇：查切削手冊(cè)表2.9，機(jī)床進(jìn)給機(jī)構(gòu)允許軸向力為8330N時(shí)，進(jìn)給量為。以上三個(gè)進(jìn)給量比較得出，受限制的進(jìn)給量是工藝要求，其值為：0.260.32mm/r。根據(jù)簡(jiǎn)明手冊(cè)表4.2-16,最終選擇進(jìn)給量。由于是通孔加工，為避免即將鉆穿時(shí)鉆頭折斷，故應(yīng)在即將鉆穿時(shí)停止自動(dòng)進(jìn)給而改為手動(dòng)進(jìn)給。根據(jù)切削手冊(cè)表2.19查出,鉆孔時(shí)軸向力Ff=1760N，軸向力修正系數(shù)為1.0，故Ff=1760N。根據(jù)Z525立式鉆床使用說明書，機(jī)床進(jìn)給機(jī)構(gòu)允許的最大軸向力為8830NFf，故所選進(jìn)給量可用。2.2 確定鉆頭磨鈍標(biāo)準(zhǔn)及壽命后刀面最大磨損限度（查簡(jiǎn)明手冊(cè)）為0.6mm，壽命2.3 切削速度查切削手冊(cè)表2.30，切削速度計(jì)算公式為： （m/min）其中，查得修正系數(shù)：，故實(shí)際的切削速度： 2.4 檢驗(yàn)機(jī)床扭矩及功率查切削手冊(cè)表2.20，當(dāng)f0.33, do11mm時(shí)，Mt=31.78Nm，修正系數(shù)均為1.0，故MC=31.78 Nm。查機(jī)床使用說明書：Mm =72.6 Nm。查切削手冊(cè)表2.23,鉆頭消耗功率：Pc=1.0kw。查機(jī)床使用說明書，。由于，故切削用量可用，即：，3、計(jì)算工時(shí)3 鉆16孔，孔深為10mm，與11形成沉孔2.1 粗鉆16孔 2.1.1選擇鉆頭根據(jù)切削手冊(cè)表2.1.2.2，選擇高速鋼麻花鉆鉆頭，粗鉆時(shí)do=15mm，鉆頭采用雙錐后磨橫刀，后角o12，二重刃長度b=2.5mm,橫刀長b=1.5mm,寬l=3mm,棱帶長度， 2.2 選擇切削用量 2.2.1 確定進(jìn)給量按加工要求確定進(jìn)給量：查切削手冊(cè)，由切削手冊(cè)表2.7,系數(shù)為0.5,則： 按鉆頭強(qiáng)度選擇:查切削手冊(cè)表2.8,鉆頭允許進(jìn)給量為：；按機(jī)床進(jìn)給機(jī)構(gòu)強(qiáng)度選擇：查切削手冊(cè)表2.9，機(jī)床進(jìn)給機(jī)構(gòu)允許軸向力為8330N時(shí)，進(jìn)給量為。以上三個(gè)進(jìn)給量比較得出，受限制的進(jìn)給量是工藝要求，其值為：0.3050.375mm/r。根據(jù)簡(jiǎn)明手冊(cè)表4.2-16,最終選擇進(jìn)給量。根據(jù)切削手冊(cè)表2.19查出,鉆孔時(shí)軸向力Ff=2500N，軸向力修正系數(shù)為1.0，故Ff=2500N。根據(jù)Z525立式鉆床使用說明書，機(jī)床進(jìn)給機(jī)構(gòu)允許的最大軸向力為8830NFf，故所選進(jìn)給量可用。2.2.2 確定鉆頭磨鈍標(biāo)準(zhǔn)及壽命后刀面最大磨損限度（查簡(jiǎn)明手冊(cè)）為0.62mm，壽命2.2.3 切削速度查切削手冊(cè)表2.30，切削速度計(jì)算公式為： （m/min）其中，查得修正系數(shù)：，故實(shí)際的切削速度： 2.2.4 檢驗(yàn)機(jī)床扭矩及功率查切削手冊(cè)表2.20，當(dāng)f0.41, do16mm時(shí)，Mt=31.78Nm，修正系數(shù)均為1.0，故MC=31.78 Nm。查機(jī)床使用說明書：Mm =52 Nm。查切削手冊(cè)表2.23,鉆頭消耗功率：Pc=1.3kw。查機(jī)床使用說明書，。由于，故切削用量可用，即：，3、計(jì)算工時(shí)3.2 粗鉸16孔粗鉸至16mm刀具：專用鉸刀專用鉸刀機(jī)床：Z525立式鉆床根據(jù)有關(guān)手冊(cè)的規(guī)定，鉸刀的進(jìn)給量為0.81.2mm/z,進(jìn)給量取0.81mm/r，機(jī)床主軸轉(zhuǎn)速取為=392r/min，則其切削速度為：。機(jī)動(dòng)時(shí)切削工時(shí)，=18mm，工序5 鉆，鉸8孔，保證孔的精度1. 鉆8孔 1.1選擇鉆頭根據(jù)切削手冊(cè)表2.1.2.2，選擇高速鋼麻花鉆鉆頭，粗鉆時(shí)do=7.8mm，鉆頭采用雙錐后磨橫刀1.2 選擇切削用量 查切削手冊(cè)，f=0.360.44mm/r， l/d=20/8=2.5 ，由切削手冊(cè)表2.7，系數(shù)為0.5，則f=（0.360.44）*0.5=0.180.22mm/r 根據(jù)簡(jiǎn)明手冊(cè)表4.2-16 ，最終選擇f=0.22mm/r 1.3 確定鉆頭磨鈍標(biāo)準(zhǔn)及壽命后刀面最大磨損限度（查簡(jiǎn)明手冊(cè)）為0.6mm，壽命1.4 切削速度 查切削手冊(cè)表2.30，切削速度計(jì)算公式為： （m/min）其中，查得修正系數(shù)：，故實(shí)際的切削速度： （4）檢驗(yàn)機(jī)床扭矩及功率查切削手冊(cè)表2.20，當(dāng)f0.26, do11mm時(shí)，Mt=10.94Nm，修正系數(shù)均為1.0，故MC=10.94 Nm。查機(jī)床使用說明書：Mm =144.2 Nm。查切削手冊(cè)表2.23,鉆頭消耗功率：Pc=1.0kw。查機(jī)床使用說明書，。由于，故切削用量可用，即：，3、計(jì)算工時(shí)2. 粗鉸至7.96mm 刀具：專用鉸刀機(jī)床：Z525立式鉆床根據(jù)有關(guān)手冊(cè)的規(guī)定，鉸刀的進(jìn)給量為0.71.1mm/z,進(jìn)給量取0.81mm/r，機(jī)床主軸轉(zhuǎn)速取為=1360r/min，則其切削速度為：。機(jī)動(dòng)時(shí)切削工時(shí)，=26mm，(2) 精鉸至刀具：機(jī)床：Z525立式鉆床根據(jù)有關(guān)手冊(cè)的規(guī)定，鉸刀的進(jìn)給量取0.22mm/r，機(jī)床主軸轉(zhuǎn)速取為：=1136r/min，則其切削速度為：機(jī)動(dòng)時(shí)切削工時(shí)，=26mm工序6 粗鏜，半精鏜32孔，以刀架底面為定位基準(zhǔn)1. 粗鏜32孔機(jī)床：T616臥式鏜床單邊余量,可一次切除，則 。由切削手冊(cè)表1.5查得，進(jìn)給量取為0.52mm/r。由切削手冊(cè)表1.1查得 Vt=114,mm/min Kv=1.0*1.2*0.8*0.8*1.2*1.0=0.92 則： Vc=114*0.92=105m/min 查簡(jiǎn)明手冊(cè)表4.2-20，取為1160r/min。加工基本工時(shí)：2半精鏜32孔機(jī)床：T616臥式鏜床單邊余量,可一次切除，則 。由切削手冊(cè)表1.5查得，進(jìn)給量取為0.145mm/r。由切削手冊(cè)表1.1查得 Vt=163,mm/min Kv=1.0*1.2*0.8*0.8*1.2*1.0=0.92 則： Vc=163*0.92=150m/min 查簡(jiǎn)明手冊(cè)表4.2-20，取為1160r/min。加工基本工時(shí)：工序7 鉆M8底孔，攻螺紋1. 鉆螺紋底孔6.80mm機(jī)床：Z525立式鉆床刀具：高速鋼麻花鉆根據(jù)切削手冊(cè)查得，進(jìn)給量為0.360.44mm/z, 系數(shù)為0.5，故f=（0.360.44）*0.5=0.180.22mm/z ，現(xiàn)取f=0.22mm/z，v=28m/min，則：查簡(jiǎn)明手冊(cè)表4.2-15，取。所以實(shí)際切削速度為：計(jì)算切削基本工時(shí)：2攻螺紋M8機(jī)床：Z525立式鉆床刀具：絲錐M8，P=1.25mm切削用量選為：，機(jī)床主軸轉(zhuǎn)速為：Ns=1000V/3.14*8=239r/min， 按機(jī)床使用說明書選?。海瑒t ；機(jī)動(dòng)時(shí)，計(jì)算切削基本工時(shí)：6.夾具設(shè)計(jì)為了提高勞動(dòng)生產(chǎn)率，保證加工質(zhì)量，降低勞動(dòng)強(qiáng)度，需要設(shè)計(jì)專用夾具。并設(shè)計(jì)工序7鉆M8螺紋底孔的夾具。本夾具將用于Z525立式鉆床，刀具為高速鋼麻花鉆。6.1 問題的提出夾具是一種裝夾工件的工藝裝備，它廣泛地應(yīng)用于機(jī)械制造過程地切削加工、 熱處理、裝配等工藝過程中。機(jī)床夾具按在不同生產(chǎn)類型中的通用性，可以分為通用夾具. 專用夾具. 可調(diào)夾具. 組合夾具等。本夾具主要用來鉆M8螺紋底孔，該孔是直通孔，在32孔的的正上方，由于本工序是中批生產(chǎn)，還應(yīng)考慮如何提高勞動(dòng)生產(chǎn)力，降低勞動(dòng)強(qiáng)度，而其位置尺寸為自由公差，精度不是主要問題。6.2 夾具設(shè)計(jì)6.2.1、定位基準(zhǔn)選擇 由零件圖可知，M8，為使定位誤差為零，應(yīng)該選擇以32孔的后端面為定位基準(zhǔn)，M8的孔中心線豎直垂直于32孔的水平中心線。為了提高加工效率，現(xiàn)決定采用手動(dòng)夾緊工件快換裝置，并采用快換鉆套以利于在鉆孔后攻螺紋。定位件、螺母/V形塊、夾緊螺栓等都是標(biāo)準(zhǔn)件。6.2.2、切削力及夾緊力計(jì)算 刀具：硬質(zhì)合金麻花鉆，。由實(shí)際加工的經(jīng)驗(yàn)可知,鉆削時(shí)的主要切削力為鉆頭的切削方向,即垂直于工作臺(tái),查切削手冊(cè)表2.3，切削力計(jì)算公式為： 其中：，與加工材料有關(guān),取0.94；與刀具刃磨形狀有關(guān),取1.33；與刀具磨鈍標(biāo)準(zhǔn)有關(guān),取1.0，則： 參考文獻(xiàn) 1 李旦等，機(jī)床專用夾具圖冊(cè)，哈爾濱：哈爾濱工業(yè)大學(xué)出版社，2005。2 孫已德，機(jī)床夾具圖冊(cè)，北京：機(jī)械工業(yè)出版社，1984。3 何玉林，機(jī)械制圖，重慶：重慶大學(xué)出版社，20001983。4 機(jī)械工程基礎(chǔ)與通用標(biāo)準(zhǔn)實(shí)用叢書編委會(huì)，形狀和位置公差，北京：中國計(jì)劃出版社，2004。5 淘濟(jì)賢等，機(jī)床夾具設(shè)計(jì)，北京：機(jī)械工業(yè)出版社，1986。6 李洪，機(jī)械加工工藝師手冊(cè)，北京：機(jī)械工業(yè)出版社，1990。7 機(jī)械設(shè)計(jì)手冊(cè)編委會(huì)，機(jī)械設(shè)計(jì)手冊(cè)卷4，北京：機(jī)械工業(yè)出版社，1998。8 東北重型機(jī)械學(xué)院，機(jī)床夾具設(shè)計(jì)手冊(cè)，上海：上?？茖W(xué)技術(shù)出版社，1979。9 賀光誼等，畫法幾何及機(jī)械制圖，重慶：重慶大學(xué)出版社，1994。10 丁駿一，典型零件制造工藝，北京：機(jī)械工業(yè)出版社,1989。11 孫麗媛，機(jī)械制造工藝及專用夾具設(shè)計(jì)指導(dǎo)，北京：冶金工業(yè)出版社，2002。12 東北重型機(jī)械學(xué)院等，機(jī)床夾具設(shè)計(jì)手冊(cè)，上海：上海科學(xué)技術(shù)出版社，1979。13 孟少龍，機(jī)械加工工藝手冊(cè)第1卷，北京：機(jī)械工業(yè)出版社，1991。14 金屬機(jī)械加工工藝人員手冊(cè)修訂組，金屬機(jī)械加工工藝人員手冊(cè)，上海：上?？茖W(xué)技術(shù)出版社，1979。16 馬賢智，機(jī)械加工余量與公差手冊(cè)，北京：中國標(biāo)準(zhǔn)出版社，1994。17 上海金屬切削技術(shù)協(xié)會(huì)，金屬切削手冊(cè)，上海：上?？茖W(xué)技術(shù)出版社，1984。18 周永強(qiáng)，高等學(xué)校畢業(yè)設(shè)計(jì)指導(dǎo)，北京：中國建材工業(yè)出版社，2002。33 哈爾濱理工大學(xué)機(jī) 械 加 工 工 序 卡產(chǎn)品型號(hào)零（部）件圖號(hào)共 6頁產(chǎn)品名稱刀架零（部）件名稱第 1 頁車 間工序號(hào)工序名稱材料牌號(hào)020銑上底面 45毛坯種類毛坯外形尺寸每毛坯件數(shù)每臺(tái)件數(shù)鑄件60X1041設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)立式銑床X511夾 具 編 號(hào)夾 具 名 稱切 削 液工序工時(shí)準(zhǔn)終單件序號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速(r/min)切削速度(m/min)進(jìn)給量(mm/r)切削深度(mm)走刀次數(shù)時(shí)間定額機(jī)動(dòng)輔助020粗銑軸承座底面YG硬質(zhì)合金端銑刀4871530.1841021 半精銑軸承座底面 YG6硬質(zhì)合金端銑刀5601540.131.51022 精銑軸承座底面YG6硬質(zhì)合金端銑刀10502970.411編制（日期）審核（日期）會(huì)簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽字日期標(biāo)記更改文件號(hào)簽字日期 哈爾濱理工大學(xué)機(jī) 械 加 工 工 序 卡產(chǎn)品型號(hào)零（部）件圖號(hào)共 6頁產(chǎn)品名稱刀架零（部）件名稱第 2 頁車 間工序號(hào)工序名稱材料牌號(hào)030晰后端面 45毛坯種類毛坯外形尺寸每毛坯件數(shù)每臺(tái)件數(shù)鑄件80X1041設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)立式銑床X51 1夾 具 編 號(hào)夾 具 名 稱切 削 液工序工時(shí)準(zhǔn)終單件序號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速(r/min)切削速度(m/min)進(jìn)給量(mm/r)切削深度(mm)走刀次數(shù)時(shí)間定額機(jī)動(dòng)輔助030粗銑軸承座底面YG硬質(zhì)合金端銑刀2651040.185.512.1031 半精銑軸承座后端面 YG6硬質(zhì)合金端銑刀5261920.511編制（日期）審核（日期）會(huì)簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽字日期標(biāo)記更改文件號(hào)簽字日期 哈爾濱理工大學(xué)機(jī) 械 加 工 工 序 卡產(chǎn)品型號(hào)零（部）件圖號(hào)共 6頁產(chǎn)品名稱刀架零（部）件名稱第 3 頁車 間工序號(hào)工序名稱材料牌號(hào)040鉆、鉸11，16孔 45毛坯種類毛坯外形尺寸每毛坯件數(shù)每臺(tái)件數(shù)鑄件60X1041設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)立式鉆床Z5251夾 具 編 號(hào)夾 具 名 稱切 削 液工序工時(shí)準(zhǔn)終單件序號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速(r/min)切削速度(m/min)進(jìn)給量(mm/r)切削深度(mm)走刀次數(shù)時(shí)間定額機(jī)動(dòng)輔助040 鉆11通孔高速鋼麻花鉆頭39217.30.2811.2041 粗鉆16孔 高速鋼麻花鉆頭54516.80.36111042 粗鉸16孔專用鉸刀39219.690.81111編制（日期）審核（日期）會(huì)簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽字日期標(biāo)記更改文件號(hào)簽字日期 哈爾濱理工大學(xué)機(jī) 械 加 工 工 序 卡產(chǎn)品型號(hào)零（部）件圖號(hào)共 6頁產(chǎn)品名稱刀架零（部）件名稱第 4 頁車 間工序號(hào)工序名稱材料牌號(hào)050鉆，鉸8孔 45毛坯種類毛坯外形尺寸每毛坯件數(shù)每臺(tái)件數(shù)鑄件60X1041設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)立式銑床Z3025 1夾 具 編 號(hào)夾 具 名 稱切 削 液工序工時(shí)準(zhǔn)終單件序號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速(r/min)切削速度(m/min)進(jìn)給量(mm/r)切削深度(mm)走刀次數(shù)時(shí)間定額機(jī)動(dòng)輔助050 鉆8孔高速鋼麻花鉆鉆頭27219.750.2210.69051 粗鉸至7.96mm 專用鉸刀136033.990.811052精鉸至 專用鉸刀1136340.221編制（日期）審核（日期）會(huì)簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽字日期標(biāo)記更改文件號(hào)簽字日期 哈爾濱理工大學(xué)機(jī) 械 加 工 工 序 卡產(chǎn)品型號(hào)零（部）件圖號(hào)共 6頁產(chǎn)品名稱刀架零（部）件名稱第 5 頁車 間工序號(hào)工序名稱材料牌號(hào)060粗鏜，半精鏜32孔，以軸承座底面為定位基準(zhǔn) 45毛坯種類毛坯外形尺寸每毛坯件數(shù)每臺(tái)件數(shù)鑄件60X1041設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)臥式鏜床T6161夾 具 編 號(hào)夾 具 名 稱切 削 液工序工時(shí)準(zhǔn)終單件序號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速(r/min)切削速度(m/min)進(jìn)給量(mm/r)切削深度(mm)走刀次數(shù)時(shí)間定額機(jī)動(dòng)輔助060 粗鏜32孔T616臥式鏜床10451050.526010.82061 半精鏜32孔 T616臥式鏜床14921500.145601編制（日期）審核（日期）會(huì)簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽字日期標(biāo)記更改文件號(hào)簽字日期 哈爾濱理工大學(xué)機(jī) 械 加 工 工 序 卡產(chǎn)品型號(hào)零（部）件圖號(hào)共 6頁產(chǎn)品名稱刀架零（部）件名稱第6 頁車 間工序號(hào)工序名稱材料牌號(hào)070 鉆M8底孔，攻螺紋 45毛坯種類毛坯外形尺寸每毛坯件數(shù)每臺(tái)件數(shù)鑄件60X1041設(shè)備名稱設(shè)備型號(hào)設(shè)備編號(hào)同時(shí)加工件數(shù)立式鉆床Z5251夾 具 編 號(hào)夾 具 名 稱切 削 液工序工時(shí)準(zhǔn)終單件序號(hào)工 步 內(nèi) 容工 藝 裝 備主軸轉(zhuǎn)速(r/min)切削速度(m/min)進(jìn)給量(mm/r)切削深度(mm)走刀次數(shù)時(shí)間定額機(jī)動(dòng)輔助070 鉆螺紋底孔6.80mm高速鋼麻花鉆1311280.221071 攻螺紋M6 絲錐M8，P=1.25mm239 60.22118編制（日期）審核（日期）會(huì)簽（日期）標(biāo)記處數(shù)更改文件號(hào)簽字日期標(biāo)記更改文件號(hào)簽字日期 湖南工業(yè)大學(xué) 外文翻譯專 業(yè) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 學(xué) 生 姓 名 王 曉 雄 班 級(jí) 機(jī)本0303班 學(xué) 號(hào) 26030336 指 導(dǎo) 教 師 黃 開 友 MULTI-OBJECTIVE OPTIMAL FIXTURE LAYOUTDESIGN IN A DISCRETE DOMAINDiana Pelinescu and Michael Yu WangDepartment of Mechanical EngineeringUniversity of MarylandCollege Park, MD 20742 USAE-mail: yuwangeng.umd.eduAbstractThis paper addresses a major issue in fixture layout design:to evaluate the acceptable fixture designs based on several quality criteria and to select an optimal fixture appropriate with practical demands. The performance objectives considered are related to the fundamental requirements of kinematic localization and total fixturing (form-closure) and are defined as the workpiece localization accuracy and the norm and distribution of the locator contact forces. An efficient interchange algorithm is uaed in a multiple-criteria optimization process for different practical cases, leading to proper trade-off strategies for performing fixture synthesis.I. INTRODUCTIONProper fixture design is crucial to product quality in terms of precision and accuracy in part fabrication and assembly. Fixturing systems, usually consisting of clamps and locators, must be capable to assure certain quality performances, besides of positioning and holding the workpiece throughout all the machining operations. Although there are a few design guidelines such as 3-2-1 rule, automated systems for designing fixtures based on CAD models have been slow to evolve. This article describes a research approach to automated design of a class of fixtures for 3D workpieces. The parts considered to be fixtured present an arbitrary complex geometry, and the designed fixtures are limited to the minimum number of elements required, i.e. six locators and a clamp. Furthermore, the fixels are modeled as non-frictional point contacts and are restricted to be applied within a given collection of discrete candidate locations. In general, the set of fixture locations available is assumed to be a potentially very large collection; for example, the locations might be generated by discretizingthe exterior surfaces of the workpiece. The goal of the fixture design is to determine first, from the proposed discrete domain, the feasible fixture configurations that satisfy the form-closure constraint. Secondly, the sets of acceptable fixture designs are evaluated on several criteria and optimal fixtures are selected. The performance measures considered in this work are the localization accuracy, and the norm and distribution of the locator contact forces. These objectives cover the most critical error sources encountered in a fixture design, the position errors and the unwanted stress in the part-fixture elements due to an overloaded or unbalanced force system.The optimal fixture design approach is based on a concept of optimum experiment design. The algorithm developed evaluates efficiently the admissible designs exploiting the recursive properties in localization and force analysis. The algorithm produces the optimal fixture design that meets a set of multiple performance requirements.II. RELATED WORKLiterature on general fixturing techniques is substantial, e.g., 1. The essential requirement of fixturing is the century-old concept of form closure 2, which has beenextensively studied in the field of robotics in recent years 3, 4. There are several formal methods for analyzing performance of a given fixture based on the popular screw theory, dealing with issues such as kinematic closure 5, contact types and friction effects 6. A different analysis approach based on the geometric perturbation technique was reported in 7. An automatic modular fixture design procedure based on this method was developed in 8 to include geometric access constraints in addition to kinematic closure. The problem of designing modular fixtures gained more attention lately 9. There has also been extensive research in fixture designs, focusing on workpiece and fixture structuralrigidity 6, tool accessibility and path clearance 7. The problem of fixture synthesis has been largely studied for the case of a fixed number of fixture elements (or fixels) 8, 10, particularly in the application to robotic manipulation and grasping for its obvious easons 3, 4. This article aims to be an extension of the results on the fixture design issues previously reported in 14.III. FIXTURE MODELThe fundamental performance of a fixture is characterized by the kinematic constraints imposed on the workpiece being held by the fixture. The kinematic conditions are well understood 3, 4, 5, 7, 12. For a fixture of n locators (i = 1, 2, , n), the fixture can be represented by: dy=GTdqwhere define small perturbations in the locator positions and the location of the workpiece respectively. The fixture designis defined by the locator matrixi where and ni and ri denote the surface normal and position at the ith contact point on the workpiece surface. The problem of fixture design requires the synthesis of a fixturing scheme to meet a given set of performance requirements.IV. QUALITY PERFORMANCE CRITERIA FOR A FIXTUREA. Accurate LocalizationAn essential aspect of fixture quality is to position with precision the workpiece into the fixturing system. In general the workpiece positional errors are due to the geometric variability of the part and the locators set-up errors. This paper will focus only on the workpiece positional errors due to the locator positioning errors. As an extension of the fixture model equation (eq.1), the locator positioning errors dy can be related with the workpiece localization error dq as follows:Clearly, for given source errors the workpiece positional accuracy depends only on the locator locations being independent from the clamping system, the Fisher information matrix M = GGT characterizing completely the system errors. It has been shown 12 that a suitable criterion to achieve high localization accuracy is to maximize the determinant of the information matrix (Doptimality), i.e., max(det M).B. Minimal Locator Contact ForcesAnother objective in planning a fixture layout might be to minimize all support forces at the locator contact regions throughout all the operations with complete kinematic restraint or force-closure. Locator contact forces in response to the clamping action are given as: Normalizing these forces with respect to the clamping intensity we obtain:The force-closure condition requires these forces to be always positive for each locator i of a set of n locators:Computing the norm of the locator contact forces:leads to an appropriate design objective, i.e. minNote that this objective indicates both locator and clamp positions to be determined in the optimization process.C. Balanced Locator Contact ForcesAnother significant issue in designing a fixture is that the total force acting on the workpiece have to be distributed as uniformly as possible among the locator contactregions. If p represents the mean reactive force in response to the clamp action, then we define the dispersion of the locator contact forces as:Therefore, minimizing the defined dispersion represents an objective for a balanced force-closure: min(d).V. OPTIMAL FIXTURE DESIGN WITH INTERCHANGE ALGORITHMSAs mentioned earlier, by generating on the exterior surface of the workpiece to be fixtured a set of discrete locations defined as position and orientation, we create a potential collection for the fixture elements. For example, using the information contained in the part CAD model, a discrete vector collection (unitary, normal vectors) can be generated as uniformly as possible on those surfaces accessible to the fixture components (fig.1).Figure 1: Part CAD model and global collection of candidate locations for the fixture elements.The fixture design layout will select from this collection optimal candidates for locators and clamps with respect to the performance objectives and to the kinematic closure condition. Dealing with a large number of candidate locations the task of selecting an appropriate set of fixels is very complex.As already introduced in 12, 14 an effective method for finding the desired fixture with regard to one of the previous quality objectives is the optimal pursuit method with an interchange algorithm. Due to its own limitations and to the fact that the objectives are functions with many extremes, the exchange procedure may not end up to a unique optimized fixture configuration, but to several improved designs depending on the initial layout. Therefore the solution offered by the multiple interchange with random initialization algorithm is overwhelming favorable, fact that recommends this procedure over the single interchange algorithms. The algorithm can be described as a sequence of three phases:Phase 1: Random generation of initial sets of locators.The starting layout is generated by a random selection of distinct sets, each consisting from 6 locators out of the list of N candidate locations. If the clamp is pre-determined, avalid selection is obtained through a simultaneous check for all kinematic constraints. A big initial set of proposed ocators is preferred, giving the opportunity of finding a convergent optimal solution. However from the efficiency point of view the designer has to balance the algorithm between the accuracy of the final solution and the computation time.Phase 2: Improvement by interchange.The interchange algorithms goal is to pursue for an improvement of the initial sets of locators with respect to one of the objectives. Basically, this is done iteratively by exchanging one by one the proposed locators with candidate locations from the global collection. It is also essential to consider the form-closure restraint during the exchange procedure. The process will continue as long as an improvement of the objective function is registered. Studying the effect of interchange on the proposed quality measures leads us to some efficient algebraic properties. For example, an interchange between a current locator j (j = 1,2,6) and a candidate location k (k = 1,2, ,N-6) yields changes in the optimized function such that:Thus, at each interchange the pair is selected such that the significant term that controls the function evolution is improving, e.g. max p 2jk and min pc , easing the iterative process.Phase 3: Selecting the optimal solution.Applying the interchange algorithm for each initial set of locators we will end up with several distinct solutions on the configuration scheme of the fixture, the best fixture design corresponds evidently to the maximum improvement of the objective function. It should be emphasized that this algorithm can be used sequentially for different objective functions. Depending on the objective pursued the best solution can be evident (for a single objective) or might need the designers final decision (for multiple objectives).VI. MULTI-OBJECTIVE FIXTURE LOCATOR OPTIMIZATIONIn many applications the clamp is already fixed given some practical considerations. Then with the clamp predefined, the best fixture with respect to a certain performance criterion is constructed by selecting a suitable set of locators such that a significant improvement of the objective-function is registered. Using the random interchange algorithm we can analyze the impact of the optimization process on the fixture characteristics, as well as we can select the best optimized fixture solution for a specific criterion. In analyzing the effect of random interchange algorithm on several parts, there can be made the following statistical and empirical observations.A. Multi-objective trade-offsIn some applications both localization quality and a minimum force dispersion are important. In this case we may have to use a 2-step algorithm: first max(det M) and secondly min(d). The proposed order is a consequence of the above observations. First, maximizing the determinant will automatically decrease the dispersion. Next, a decreasing in dispersion leads in a decreasing in determinant value. Therefore, during the second phase of the algorithm tradeoffs between the two objectives occur. To solve the multi-objective optimization problem the interchange algorithm is applied successively for both objectives. With the clamp pre-defined, a rigorous check for form-closure is needed after each exchange step.A following set of plots present the results when the design requirements of precision localization and uniform contact forces are considered simultaneously. Fig. 2 and Fig. 3 illustrate the global changes of the fixture characteristics during the 2-step algorithm performed on an initial collection of distinct random sets of locators, with the clamp pre-fixed. It can be noticed the advantages of using max(det M) objective as a first step: while the determinant is increasing, the norm and the dispersion of the forces are decreasing, fact benefic for the overall quality of the fixture. Furthermore the solutions are convergent, such that the candidate set of locators for the next step will be significantly reduced. On the other hand, in the second phase, when applying min(d) optimization on sets of locators with a high determinant value the only trend in the determinant evolution is a decreasing one. Therefore, during the second phase of the algorithm tradeoffs between the two objectives occur, fact expressed also through the Pareto-line plot (Fig. 3). In this case the final decision has to be left for the designer to determine the best fixture scheme.Figure 2: Changes upon the fixture characteristics applying the 2-step optimization algorithm on an initial collection of random sets of locators.Figure 3: Behavior during a 2-step random interchange algorithm for a collection of locator sets.As an example, the behavior of a single initial set of locators is studied during the interchange processes of the 2-step algorithm (Fig. 4), confirming the previous remarks. The trade-off zone is decisive in the multiobjective design. The resultant configurations of the fixture after each successive phase are presented in Fig. 5. It can be noticed that the first objective moves the locators close to the boundaries as far as possible from each other, while the second one reorients them to the surfaces interior.Figure 4: General behavior of a 2-step interchange.Figure 5: Fixture configurations during a 2-step algorithm: (a) initial, (b) after max(det M), and (c) after min(d) respectively.B. Designer decision in finalizing the fixtureDuring the second phase of the algorithm a fairly significant decrease in the determinant value is registered, so few solutions will be acceptable for the multi-objective problem. In order to overcome these problems, an active designer control during min(d) interchange procedure is recommended. Essentially, the modifications consist in controlling the exchange procedure, such that the determinant of the improved locators must be permanently greater than a certain bound, simultaneously with the check for the form-closure condition. Even considering a tight bound for the determinant, more solutions are acceptable for the design than in the uncontrolled min(d) optimization case (fig. 6). As an example, the behavior of a single set of locators is studied during the interchange process of a 2- step algorithm controlled for two different bounds of the determinant value, emphasizing the fact that in the trade off zone the designer decision is decisive in finalizing the fixture configuration (fig. 7).Figure 6: Second phase of a 2-step random interchange algorithm: uncontrolled min(d); controlled min(d).Figure 7: General behavior during a 2-step algorithm applied on a single set of locators. (a) for B1 and (b) for B2.VII. OPTIMAL FIXTURE CLAMPINGThis section deals with a more complicated problem: to search simultaneously for the optimal clamp and locators in order to achieve a required fixture quality. Varying theclamp, it is obvious that the number of combinations for possible clamp-locators candidates is increasing very much. It will be shown that this problem is manageablefor the precise localization objective. For the other objectives we will have to restrain the search of the optimal clamp inside of a small set of proposed locations, such that the optimization procedure could be handled.A. Optimal Clamp from a Set of ClampsIn some applications the clamps have certain preferred locations, therefore the need to choose the best clamp from a proposed collection might be raised. For example, lets consider that a collection of preferred clamps is given, and an optimal fixture design with respect to the highly precise localization objective is needed. It is obvious that applying a random interchange procedure successively for each clamp, we find optimal fixture configurations for each specified clamp. Comparing the determinant values offered by these fixture schemes (fig. 8), we end up by selecting an optimal clamp and its corresponding locators, constructing the best- improved fixture design (fig. 9).Figure 8: Clamp selection from a collection of clamps for single-objective design.Figure 9: The initial collection of proposed clamps; the best clamp and the corresponding locators.B. Optimal Clamp from a Set of ClampsFurthermore, by extension, the selection of the optimal clamp from a set of proposed locations with regard to the multi-objective design problem can be considered. It consists of mainly applying the random 2-step interchange algorithm consecutively for each proposed clamp.By collecting the results after applying this procedure for all the clamps, we can compare their different behavior, and select the most appropriate one. It is obvious that an optimal clamp allows only small fluctuations of the determinant while the force dispersion is decreasing significantly (fig. 10). As an example, Fig. 11 illustrates the final fixture design consisting of the best clamp selected from a proposed collection with respect to the multi-objectives and the corresponding optimal locators.Figure 11: The initial collection of proposed clamps; the best clamp and the corresponding locators.VIII. CONCLUSIONSThis article focuses on optimal design of fixture layout for 3D workpieces with an optimal random interchange algorithm. The quality objectives considered include accurate workpiece localization, minimal and balanced contact forces. The paper focuses on multi-criteria optimal design with a hierarchical approach and a combined-objective approach. The optimization processes make use of an efficient interchange algorithm. Examples are used to illustrate empirical observations with respect to the design approaches and their effectiveness. The work described here is yet complete. Since the inter-relationship between the locators and the clamps has a determinant role on the fixture quality measures, a more coherent and complete approach to study the influence of the clamp and search of the optimal clamp position is needed in future works.IX. REFERENCES1 P. D. Campbell, Basic Fixture Design. New York: Industrial Press, 1994. 2 F. Reuleaux, The Kinematics of Machinery. Dover Publications, 1963.3 B. Mishra, J. T. Schwartz, and M. Sharir, On the existence and synthesis of multifinger positive grips, Robotics Report 89, Courant Institute of Mathematical Sciences, New York University, 1986.4 X. Markenscoff, L. Ni, and C. H. Papadimitriou, The geometry of grasping, International Journal of Robotics Research, vol. 9, no. 1, pp. 61-74, 1990.5 Y.-C. Chou, V. Chandru, and M. M. 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